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FP3- Find the eigenvalues and the eigenvector for the negative eigenvalue, from this 2x2 matrix of columns (2,1) and (3,0)

Let the 2x2 matrix= A. Using the characteristic equation for A (det(A-λI)=0), find the determinant of the matrix (2-λ,1) and (3,-λ). This results in the quadratic λ^2-2λ-3 so λ=3,-1. From the definition of t...
BM
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Solve for 0<x≤2π, cos^2(x)-3cos(x)=5sin^2(x)-2, giving all answers exactly

Use the identity cos^2(x)+sin^2(x)=1, to change the 5sin^(x) into 5-5cos^2(x) and rearrange. Let y=sin(x) and solve the rearranged quadratic (6y^2-3y-3) for y and find the value of x for each solution. y= -0...
BM
Answered by Ben M. • Maths tutor
5710 Views

Solve the linear equation 12x - 4 = 3x + 2

The objective of this question is to find the solution, what is x equal to? The first thing to do is try to get all x terms on one side of the equation and all non x terms on the other. Here we have positive...
DF
Answered by Diogo F. • Maths tutor
5924 Views

Michael is saving for new iPhone. He gets £30 as pocket money per week, however he spends 20% of the whole amount for leisure and his savings only consists of the residue amount. If an iPhone costs £600 how many weeks would Michael need to save for it?

Given: £30 pounds per week 20% = 0.2 = 1/5 - spending on leisure To find: a) Residue amount (Ra) b) How many weeks does Michael need to save (Tw) Solution: a) To the find residue amount we must remove the le...
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Answered by Nikola N. • Maths tutor
3911 Views

Describe how filtration of the blood occurs at the Kidney

Due to the afferent arteriole going towards the glomerulus having a having a larger diameter than the efferent arteriole leaving the glomerulus the pressure increases in the glomerulus. This causes the small...
MS
Answered by Max S. • Biology tutor
3068 Views